Combine the milk and sugar in a 2-quart saucepan over medium heat. Heat, stirring occasionally, until the sugar has dissolved and the mixture is hot.
Add the fresh ginger and reduce the heat to low. Heat, barely simmering, for 15 minutes.
Remove from the heat and add the ground ginger. Set aside to infuse for at least 45 minutes, or until the ginger flavor suites your taste. (Remember that the flavor will not be as strong when the mixture is frozen.) Remove the pieces of ginger, add the salt, cover, and chill thoroughly.
Freeze in an ice cream maker according to the manufacturer's directions. Garnish each serving with a few strips of candied ginger, if desired.